2.1.

Study Area

Our study was conducted in the middle stream of the Heihe River Basin (HRB) at the Zhangye oasis, which is located near the city of Zhangye in the arid region of Gansu Province in northwestern China (100.10°E to 100.66°E, 38.68°N to 39.15°N). The Zhangye oasis has a semiarid climate, with an annual precipitation of $<200\mathrm{mm}$ and an annual potential ET of $\sim 1200$ to 1800 mm; the annual average temperature is $\sim 7°\mathrm{C}$.^27,28 Areas of the Gobi desert and alpine vegetation are located near the study area in the Qilian Mountains (see Fig. 1). Around the oasis, the land surface is mainly covered by maize, which has a growing season that lasts from May to September. The artificial oasis is highly heterogeneous, which impacts its thermodynamic and hydraulic features. Consequently, its water use efficiency and ET are variable. The HRB has long served as a test area for integrated watershed studies and land surface and hydrological experiments.²⁸ One major objective of the Heihe Watershed Allied Telemetry Experimental Research (HiWATER), namely the Multi-Scale Observation Experiment on ET (HiWATER-MUSOEXE), is to capture strong land surface heterogeneities and the associated uncertainties within a watershed.^29–31

Fig. 1

Study area and distribution of ground observation stations in HiWATER-MUSOEXE.

2.2.

Datasets

The data in this study were mainly derived from VIIRS and MODIS. We combined these two sensors datasets with ancillary data and in situ HiWATER-MUSOEXE data to estimate and validate the VIIRS and MODIS heat fluxes.

3.1.

Pixel Evapotranspiration Algorithm

The SEB describes the transfer of energy between the land surface and the atmosphere. The energy budget is commonly expressed as follows:

Fig. 2

Flowchart of ET retrieval based on VIIRS data.

$R_n$, also known as the radiation balance or radiation budget, is the main energy source of land surface heat and mass transfers and exchanges, such as evaporation, and is calculated as the difference between the incoming and outgoing radiation

$G$ is the heat exchange between the surface and the deeper soils and is related to the exchanges of water and heat within the soil. Generally, heat is transferred from deeper depths to the surface at night. Studies have found that soil heat flux is correlated with $R_n$ and can be derived using land surface parameters.¹⁵ Because canopies exert significant influences on $G$, the fractional canopy coverage $f_c$ is used to determine the ratio of $G$ to $R_n$¹⁴

$H$ is the turbulent heat transfer between the surface and the atmosphere that is derived using the temperature gradient between them. According to gradient diffusion theory

3.2.

Accuracy Evaluation Index

To control model inputs and analyze error sources, the land surface temperature, net radiation, and soil heat flux were evaluated using in situ data. The analyses were performed using the root mean square error (RMSE), the mean bias error (MBE), and the coefficient of determination ($R^2$)

The ground-based land surface temperature ($T_s$) was calculated using the Stefan–Boltzmann law from the AMS measurements of the longwave radiation fluxes²⁵

4.1.

Evaluation of Surface Variables

The station validation results of two LSTs are shown in Tables 3 and 4. The $R^2$, MBE, and RMSE values of the VIIRS LST data are 0.77, 0.55 K, and 2.40 K, respectively. As shown in Table 3, the VIIRS MBE varies from $-6.67$ to 1.95 K; the RMSE varies from 1.16 to 7.10 K. The VIIRS LSTs are warmer than the ground LSTs for most stations. From Table 4, the MBE values for the MODIS LST are negative for most stations, and the MBEs and RMSEs are much larger, with two stations (GB and SSW) showing $\mathrm{MBEs}>2\mathrm{K}$ and $\mathrm{RMSEs}>3\mathrm{K}$. From Fig. 1, the land cover of GB and SSW is uncultivated land. In our study area, the Gobi region and desert area comprise uncultivated land. Therefore, the MODIS LST products underestimate the LSTs for barren surfaces during the daytime, consistent with the results of Refs. 25 and 44. There are two possible reasons for the large Terra MODIS LST errors over barren surface sites. First, the LST product algorithm does not cover the wide range of LSTs, i.e., the daytime LSTs are greater than the air temperature at the surface level by $>16\mathrm{K}$, which is beyond the upper limit. Second, the large errors are present in the surface emissivity values in MODIS bands 31 and 32 estimated from land cover types.⁴⁴

Table 3

The station validation of VIIRS LST.

Table 4

The station validation of MODIS LST.

As shown in Tables 3 and 4, the EC4 accuracy of both LST products is low. The main causes of the large errors are as follows: (1) buildings and soil/vegetation are distinct materials, and the emissivity algorithm may not be suitable for buildings and (2) the EC4 foundation is nonuniform and is not suitable for validation. After removing the EC4 data, the $R^2$, MBE, and RMSE values of the VIIRS LST data are 0.86, 0.75 K, and 1.97 K, respectively, and the $R^2$, MBE, and RMSE values of the MODIS LST data are 0.82, $-0.87\mathrm{K}$, and 2.77 K, respectively. The SD errors for both were large due to large errors on particular days. For example, although it was briefly cloudy above station SD on July 27, this area was not identified as cloudy in the cloud detection process.

The validation of net radiation and soil heat flux based on scatterplots is shown in Fig. 3. As shown in this figure, the $R^2$, MBE, and RMSE values of the $R_n$ calculated using the VIIRS data were 0.68, $-8.44\mathrm{W}{\mathrm{m}}^{-2}$, and $40.80\mathrm{W}{\mathrm{m}}^{-2}$, respectively, whereas the errors in the $R_n$ estimates obtained using the MODIS data were 0.64, $-33.87\mathrm{W}{\mathrm{m}}^{-2}$, and $55.25\mathrm{W}{\mathrm{m}}^{-2}$, respectively. According to the sensitivity analysis of Eq. (2), $R_s\downarrow$ and $R_L\downarrow$ are highly sensitive variables when calculating $R_n$, whereas the albedo, LST are not as sensitive. However, the $R_s\downarrow$ and $R_L\downarrow$ values used in the ET model are derived from ground observations; thus, the $R_s\downarrow$ and $R_L\downarrow$ are relatively accurate. Therefore, LST and albedo are the main sources of error and are discussed in Sec. 4.3. A 1 K bias in LST would result in an $R_n$ error of $-0.96\%$, but an albedo bias of 0.03 can lead to an $R_n$ error of $\sim 20\mathrm{W}{\mathrm{m}}^{-2}$ when the incoming solar radiation is large. Studies have shown that land surface albedos retrieved using VIIRS data are better than those retrieved using MODIS;²⁶ thus, the $R_n$ values calculated using the VIIRS data show better results.

Fig. 3

Comparison of the $R_n$ and $G$ data derived from the two sensors with measured data.

The $R^2$, MBE, and RMSE values of $G$ calculated using the VIIRS data were 0.58, $-11.80\mathrm{W}{\mathrm{m}}^{-2}$, and $30.84\mathrm{W}{\mathrm{m}}^{-2}$, respectively, whereas the errors in the $G$ values calculated using the MODIS data were 0.52, $-20.47\mathrm{W}{\mathrm{m}}^{-2}$, and $40.98\mathrm{W}{\mathrm{m}}^{-2}$, respectively. Since $G$ is calculated using $R_n$, $G$ and $R_n$ show the same sensitivity results. As shown in the validation of $G$ in Fig. 3, the sensor-retrieved $G$ is overestimated at many sites, which may be related to the soil temperature and moisture above the soil heat plates at each site. For example, at EC5, the soil temperature and moisture were the same at different depths after July 19, which resulted in the surface $G$ being equal to the $G$ at a depth of 6 cm. However, the $G$ values below the surface are usually less than those at the soil surface; thus, the validation results of $G$ at EC5 indicate that $G$ was overestimated. However, $G$ is still underestimated as a whole ($\mathrm{MBE}<0$) because $R_n$ is also underestimated.

4.2.

Validation of Sensible Heat Fluxes

Figure 4 provides the turbulent heat flux results calculated from VIIRS and MODIS on June 19, 2012. The differences in the distributions of the heat fluxes calculated from the two sensors are not obvious because they follow certain underlying rules. Specifically, the spatial distributions of the turbulent heat fluxes are related to their underlying land covers. $H$ values are higher in areas covered by buildings and uncultivated land, including land patches in the desert areas, barren areas, and Gobi regions. However, $H$ values are lower in the water-covered and agricultural areas within the oasis. Comparing Figs. 4(e) and 4(f) and Figs. 4(g) and 4(h), we see that the $H$ values (LE values) of the barren areas in the southwest are lower (higher) than those of the desert areas in the southeast, although both areas were classified as uncultivated land. Because the barren areas in the southwest border of the Qilian Mountains, the groundwater levels are high due to snow melt and the downward movement of water, leading to a soil moisture content of $\sim 30\%$ according to in situ measurements at a depth of 2 cm.¹⁴ As shown in Figs. 4(e) and 4(f), some areas in the $H$ distribution map have values less than zero due to inversion from the oasis effect or irrigation. The HiWATER soil moisture data show that irrigation occurred on June 19, 2012. Irrigation is the main source of water within the oasis and cools the land surface to temperatures below that of the air.

Fig. 4

Maps of the turbulent heat fluxes (a) and (b) calculated by VIIRS and (c) and (d) calculated by MODIS on June 19, 2012.

To further analyze the heat fluxes retrieved from the two sensors, the $H$ values were evaluated using in situ data. In recent years, many researchers have employed a footprint model to validate remote sensing-based ET estimates (specifically only $H$ and $LE$). When combined with the flux contribution source areas, this model solves the problems associated with mismatches between the observed values and the remote sensing-based estimates and leads to better results.^45,46 In this study, we employ the path-weighting function of the LAS and the footprint model for point fluxes to calculate the LAS source area.^30,46 The station-validated results for the $H$ values are shown in Fig. 5.

Fig. 5

Comparison of the sensible heat fluxes derived from the two sensors with measured data.

The footprint validation results show that the $R^2$, MBE, and RMSE values of the $H$ values calculated using the VIIRS data were 0.68, $15.23\mathrm{W}{\mathrm{m}}^{-2}$, and $39.55\mathrm{W}{\mathrm{m}}^{-2}$, respectively, and those of the MODIS-based $H$ values were 0.56, $-29.36\mathrm{W}{\mathrm{m}}^{-2}$, and $50.81\mathrm{W}{\mathrm{m}}^{-2}$, respectively. Compared with the observed values, the $H$ calculated using VIIRS data is overestimated ($\mathrm{MBE}>0$), whereas the $H$ calculated using MODIS data is underestimated. The reason is related to the LST. According to Eq. (4), $H$ is most sensitive to the LST values. A 1 K bias in LST would result in an error in $H$ of 20.5%. Consequently, LST is the most important factor affecting $H$. However, this sensitivity to LST is unstable and depends on the strength of the turbulence present, as discussed in Sec. 4.3. The validation of the VIIRS and MODIS surface temperature products in Sec. 4.1 shows that the VIIRS LSTs are warmer than the ground LSTs (with an average bias of 0.55 K), whereas the Terra MODIS LSTs are significantly underestimated (with an average bias of $-1.22\mathrm{K}$).

4.3.

Error and Sensitivity Analysis

Many sources of error are unavoidable, including the calibration coefficients of the onboard satellite sensors; the drifts in the sensors caused by the aging of the instruments; mismatches in the timescales of the observational data, which are averaged over time, and the remotely sensed turbulent heat fluxes, which are instantaneous; and the geometric corrections cause a half-pixel bias less than or equal to the deviation of the artificially subjective interpretation. The estimation of $H$ is the most important and difficult step in the remote sensing-based assessment of the SEB; thus, the sensitivity of $H$ was analyzed first. Land surface variables, including LST, canopy height, FVC, and LAI, and meteorological variables, including wind speed, air temperature, and relative humidity, are the major factors in the sensitivity analysis of $H$. Figure 6 presents a sensitivity analysis of $H$. In this case, the average LST is 304 K, with a range from 297.5 to 311 K, and has a step size of 0.5 K; meanwhile, LAI ranges from 0.1 to 2.5 and has a step size of 0.1. The canopy height is 1 m, with a range from 0.1 to 1.9 m. The wind speed ranges from 0.50 to $4.95\mathrm{m}{\mathrm{s}}^{-1}$, the air temperature is $T_a=297.90\mathrm{K}$, $\mathrm{FVC}=0.54$, and the relative humidity is $\mathrm{RH}=40.29\%$. In addition, the land cover is maize and the reference $H$ is $250.05\mathrm{W}{\mathrm{m}}^{-2}$.

Fig. 6

Sensitivity analysis of the surface variables for the sensible heat flux.

The air pressure is stable over short periods and has little effect on the ET results. Although, $H$ is sensitive to meteorological variables, such as wind speed and air temperature (see Fig. 6), the meteorological data used in the ET model are derived from ground observations; thus, the meteorological factors are relatively accurate. As shown in Fig. 6, LAI, LST, and the canopy height are all influential variables. $H$ is sensitive to LAI when LAI is $<1$. The momentum roughness length increases as LAI increases and the turbulent exchange is enhanced. However, when LAI is $>1$, the plant canopy is regarded as a continuum that is not a sensitive variable. Because our study area is dominated by agriculture and the study period extended from June to September, the crops in the middle reaches of the HRB grew quickly; thus, LAI was usually $>1$. Hence, LST and canopy height are the main sources of error.

As discussed above, the accuracy of the LST and canopy height parameters greatly influences the estimated turbulent heat flux. Since the VIIRS sensor is still running, the algorithm to calculate its LST product is still being explored.²⁵ Canopy heights are known a priori and are derived from phenophase classifications; these classifications influence the accuracies of the surface roughness calculations. Multisource remote sensing data, such as active microwave and LiDAR data, can be used to obtain canopy heights for future studies,¹⁴ which would lead to more robust canopy height values. Since a footprint model was used in the validation, discrepancies between the in situ measurements and remote sensing pixels still exist in the footprints.³

Additionally, to correct the discrepancies between the remotely sensed radiative surface temperatures and the aerodynamic temperatures at the source of heat transport, a brief and well-constrained parameterization scheme (under a uniform and flat plant surface) that included excess resistance was used to calculate the aerodynamic resistance of the heat transfer.¹⁴ Since the surface cover of the HRB is very heterogeneous,^4,30 multiple parameterization methods should be compared to select an optimal method.⁴³ Although these preliminary results show that VIIRS data have certain advantages over MODIS data when calculating surface heat fluxes, the limited ground observation data in this paper use only 9 days in calculating and validating the results. Future work will involve testing this single-source ET estimation algorithm and the practicality of VIIRS data for calculating the heat fluxes in the range of actual environmental conditions.